LMFDB - Embedded newform 975.2.a.p.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(1,975)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("975.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 3 $ x^3 - x^2 - 5*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.571993$ of defining polynomial
Character	$\chi$	$=$	975.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.571993 q^{2} +1.00000 q^{3} -1.67282 q^{4} +0.571993 q^{6} +1.42801 q^{7} -2.10083 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.571993 q^{2} +1.00000 q^{3} -1.67282 q^{4} +0.571993 q^{6} +1.42801 q^{7} -2.10083 q^{8} +1.00000 q^{9} +3.24482 q^{11} -1.67282 q^{12} +1.00000 q^{13} +0.816810 q^{14} +2.14399 q^{16} +1.85601 q^{17} +0.571993 q^{18} -1.81681 q^{19} +1.42801 q^{21} +1.85601 q^{22} -1.52884 q^{23} -2.10083 q^{24} +0.571993 q^{26} +1.00000 q^{27} -2.38880 q^{28} +2.34565 q^{29} +6.38880 q^{31} +5.42801 q^{32} +3.24482 q^{33} +1.06163 q^{34} -1.67282 q^{36} +3.52884 q^{37} -1.03920 q^{38} +1.00000 q^{39} -3.81681 q^{41} +0.816810 q^{42} +10.0185 q^{43} -5.42801 q^{44} -0.874485 q^{46} +11.2633 q^{47} +2.14399 q^{48} -4.96080 q^{49} +1.85601 q^{51} -1.67282 q^{52} +6.81681 q^{53} +0.571993 q^{54} -3.00000 q^{56} -1.81681 q^{57} +1.34169 q^{58} -5.91764 q^{59} +5.48963 q^{61} +3.65435 q^{62} +1.42801 q^{63} -1.18319 q^{64} +1.85601 q^{66} -10.3025 q^{67} -3.10478 q^{68} -1.52884 q^{69} -9.81681 q^{71} -2.10083 q^{72} +5.32718 q^{73} +2.01847 q^{74} +3.03920 q^{76} +4.63362 q^{77} +0.571993 q^{78} -2.96080 q^{79} +1.00000 q^{81} -2.18319 q^{82} +3.14003 q^{83} -2.38880 q^{84} +5.73050 q^{86} +2.34565 q^{87} -6.81681 q^{88} -4.85601 q^{89} +1.42801 q^{91} +2.55748 q^{92} +6.38880 q^{93} +6.44252 q^{94} +5.42801 q^{96} +1.51037 q^{97} -2.83754 q^{98} +3.24482 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + 5 q^{4} + q^{6} + 5 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + 5 * q^4 + q^6 + 5 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + 5 q^{4} + q^{6} + 5 q^{7} + 3 q^{8} + 3 q^{9} - q^{11} + 5 q^{12} + 3 q^{13} - 9 q^{14} + 5 q^{16} + 7 q^{17} + q^{18} + 6 q^{19} + 5 q^{21} + 7 q^{22} + 4 q^{23} + 3 q^{24} + q^{26} + 3 q^{27} + 5 q^{28} - 13 q^{29} + 7 q^{31} + 17 q^{32} - q^{33} - 19 q^{34} + 5 q^{36} + 2 q^{37} - 16 q^{38} + 3 q^{39} - 9 q^{42} - 17 q^{44} + 26 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} + 7 q^{51} + 5 q^{52} + 9 q^{53} + q^{54} - 9 q^{56} + 6 q^{57} - 11 q^{58} + 3 q^{59} - 5 q^{61} + 31 q^{62} + 5 q^{63} - 15 q^{64} + 7 q^{66} - 3 q^{67} + 5 q^{68} + 4 q^{69} - 18 q^{71} + 3 q^{72} + 26 q^{73} - 24 q^{74} + 22 q^{76} - 9 q^{77} + q^{78} + 4 q^{79} + 3 q^{81} - 18 q^{82} + 13 q^{83} + 5 q^{84} - 10 q^{86} - 13 q^{87} - 9 q^{88} - 16 q^{89} + 5 q^{91} + 32 q^{92} + 7 q^{93} - 5 q^{94} + 17 q^{96} + 26 q^{97} - 40 q^{98} - q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + 5 * q^4 + q^6 + 5 * q^7 + 3 * q^8 + 3 * q^9 - q^11 + 5 * q^12 + 3 * q^13 - 9 * q^14 + 5 * q^16 + 7 * q^17 + q^18 + 6 * q^19 + 5 * q^21 + 7 * q^22 + 4 * q^23 + 3 * q^24 + q^26 + 3 * q^27 + 5 * q^28 - 13 * q^29 + 7 * q^31 + 17 * q^32 - q^33 - 19 * q^34 + 5 * q^36 + 2 * q^37 - 16 * q^38 + 3 * q^39 - 9 * q^42 - 17 * q^44 + 26 * q^46 - 7 * q^47 + 5 * q^48 - 2 * q^49 + 7 * q^51 + 5 * q^52 + 9 * q^53 + q^54 - 9 * q^56 + 6 * q^57 - 11 * q^58 + 3 * q^59 - 5 * q^61 + 31 * q^62 + 5 * q^63 - 15 * q^64 + 7 * q^66 - 3 * q^67 + 5 * q^68 + 4 * q^69 - 18 * q^71 + 3 * q^72 + 26 * q^73 - 24 * q^74 + 22 * q^76 - 9 * q^77 + q^78 + 4 * q^79 + 3 * q^81 - 18 * q^82 + 13 * q^83 + 5 * q^84 - 10 * q^86 - 13 * q^87 - 9 * q^88 - 16 * q^89 + 5 * q^91 + 32 * q^92 + 7 * q^93 - 5 * q^94 + 17 * q^96 + 26 * q^97 - 40 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.571993	0.404460	0.202230	−	0.979338i	$-0.435181\pi$
$2$	0.571993	0.404460	0.202230	+	0.979338i	$0.435181\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.67282	−0.836412
$5$	0	0
$5$	0	0
$6$	0.571993	0.233515
$7$	1.42801	0.539736	0.269868	−	0.962897i	$-0.413020\pi$
$7$	1.42801	0.539736	0.269868	+	0.962897i	$0.413020\pi$
$8$	−2.10083	−0.742756
$9$	1.00000	0.333333
$10$	0	0
$11$	3.24482	0.978349	0.489175	−	0.872186i	$-0.337298\pi$
$11$	3.24482	0.978349	0.489175	+	0.872186i	$0.337298\pi$
$12$	−1.67282	−0.482903
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.816810	0.218302
$15$	0	0
$16$	2.14399	0.535997
$17$	1.85601	0.450149	0.225075	−	0.974342i	$-0.427737\pi$
$17$	1.85601	0.450149	0.225075	+	0.974342i	$0.427737\pi$
$18$	0.571993	0.134820
$19$	−1.81681	−0.416805	−0.208402	−	0.978043i	$-0.566826\pi$
$19$	−1.81681	−0.416805	−0.208402	+	0.978043i	$0.566826\pi$
$20$	0	0
$21$	1.42801	0.311617
$22$	1.85601	0.395703
$23$	−1.52884	−0.318785	−0.159392	−	0.987215i	$-0.550953\pi$
$23$	−1.52884	−0.318785	−0.159392	+	0.987215i	$0.550953\pi$
$24$	−2.10083	−0.428830
$25$	0	0
$26$	0.571993	0.112177
$27$	1.00000	0.192450
$28$	−2.38880	−0.451441
$29$	2.34565	0.435576	0.217788	−	0.975996i	$-0.430116\pi$
$29$	2.34565	0.435576	0.217788	+	0.975996i	$0.430116\pi$
$30$	0	0
$31$	6.38880	1.14746	0.573731	−	0.819043i	$-0.305495\pi$
$31$	6.38880	1.14746	0.573731	+	0.819043i	$0.305495\pi$
$32$	5.42801	0.959545
$33$	3.24482	0.564850
$34$	1.06163	0.182068
$35$	0	0
$36$	−1.67282	−0.278804
$37$	3.52884	0.580137	0.290069	−	0.957006i	$-0.406322\pi$
$37$	3.52884	0.580137	0.290069	+	0.957006i	$0.406322\pi$
$38$	−1.03920	−0.168581
$39$	1.00000	0.160128
$40$	0	0
$41$	−3.81681	−0.596086	−0.298043	−	0.954553i	$-0.596334\pi$
$41$	−3.81681	−0.596086	−0.298043	+	0.954553i	$0.596334\pi$
$42$	0.816810	0.126037
$43$	10.0185	1.52780	0.763901	−	0.645333i	$-0.223281\pi$
$43$	10.0185	1.52780	0.763901	+	0.645333i	$0.223281\pi$
$44$	−5.42801	−0.818303
$45$	0	0
$46$	−0.874485	−0.128936
$47$	11.2633	1.64292	0.821460	−	0.570267i	$-0.193160\pi$
$47$	11.2633	1.64292	0.821460	+	0.570267i	$0.193160\pi$
$48$	2.14399	0.309458
$49$	−4.96080	−0.708685
$50$	0	0
$51$	1.85601	0.259894
$52$	−1.67282	−0.231979
$53$	6.81681	0.936361	0.468180	−	0.883633i	$-0.344910\pi$
$53$	6.81681	0.936361	0.468180	+	0.883633i	$0.344910\pi$
$54$	0.571993	0.0778384
$55$	0	0
$56$	−3.00000	−0.400892
$57$	−1.81681	−0.240642
$58$	1.34169	0.176173
$59$	−5.91764	−0.770411	−0.385206	−	0.922831i	$-0.625869\pi$
$59$	−5.91764	−0.770411	−0.385206	+	0.922831i	$0.625869\pi$
$60$	0	0
$61$	5.48963	0.702876	0.351438	−	0.936211i	$-0.385693\pi$
$61$	5.48963	0.702876	0.351438	+	0.936211i	$0.385693\pi$
$62$	3.65435	0.464103
$63$	1.42801	0.179912
$64$	−1.18319	−0.147899
$65$	0	0
$66$	1.85601	0.228459
$67$	−10.3025	−1.25865	−0.629325	−	0.777142i	$-0.716668\pi$
$67$	−10.3025	−1.25865	−0.629325	+	0.777142i	$0.716668\pi$
$68$	−3.10478	−0.376510
$69$	−1.52884	−0.184050
$70$	0	0
$71$	−9.81681	−1.16504	−0.582521	−	0.812816i	$-0.697933\pi$
$71$	−9.81681	−1.16504	−0.582521	+	0.812816i	$0.697933\pi$
$72$	−2.10083	−0.247585
$73$	5.32718	0.623499	0.311749	−	0.950164i	$-0.399085\pi$
$73$	5.32718	0.623499	0.311749	+	0.950164i	$0.399085\pi$
$74$	2.01847	0.234642
$75$	0	0
$76$	3.03920	0.348621
$77$	4.63362	0.528050
$78$	0.571993	0.0647655
$79$	−2.96080	−0.333116	−0.166558	−	0.986032i	$-0.553265\pi$
$79$	−2.96080	−0.333116	−0.166558	+	0.986032i	$0.553265\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.18319	−0.241093
$83$	3.14003	0.344663	0.172332	−	0.985039i	$-0.444870\pi$
$83$	3.14003	0.344663	0.172332	+	0.985039i	$0.444870\pi$
$84$	−2.38880	−0.260640
$85$	0	0
$86$	5.73050	0.617935
$87$	2.34565	0.251480
$88$	−6.81681	−0.726674
$89$	−4.85601	−0.514736	−0.257368	−	0.966313i	$-0.582855\pi$
$89$	−4.85601	−0.514736	−0.257368	+	0.966313i	$0.582855\pi$
$90$	0	0
$91$	1.42801	0.149696
$92$	2.55748	0.266635
$93$	6.38880	0.662488
$94$	6.44252	0.664496
$95$	0	0
$96$	5.42801	0.553994
$97$	1.51037	0.153354	0.0766772	−	0.997056i	$-0.475569\pi$
$97$	1.51037	0.153354	0.0766772	+	0.997056i	$0.475569\pi$
$98$	−2.83754	−0.286635
$99$	3.24482	0.326116
$100$	0	0
$101$	−17.0185	−1.69340	−0.846701	−	0.532070i	$-0.821414\pi$
$101$	−17.0185	−1.69340	−0.846701	+	0.532070i	$0.821414\pi$
$102$	1.06163	0.105117
$103$	−9.73050	−0.958774	−0.479387	−	0.877603i	$-0.659141\pi$
$103$	−9.73050	−0.958774	−0.479387	+	0.877603i	$0.659141\pi$
$104$	−2.10083	−0.206003
$105$	0	0
$106$	3.89917	0.378721
$107$	−3.43196	−0.331780	−0.165890	−	0.986144i	$-0.553050\pi$
$107$	−3.43196	−0.331780	−0.165890	+	0.986144i	$0.553050\pi$
$108$	−1.67282	−0.160968
$109$	−2.96080	−0.283593	−0.141796	−	0.989896i	$-0.545288\pi$
$109$	−2.96080	−0.283593	−0.141796	+	0.989896i	$0.545288\pi$
$110$	0	0
$111$	3.52884	0.334942
$112$	3.06163	0.289297
$113$	−9.54731	−0.898135	−0.449068	−	0.893498i	$-0.648244\pi$
$113$	−9.54731	−0.898135	−0.449068	+	0.893498i	$0.648244\pi$
$114$	−1.03920	−0.0973303
$115$	0	0
$116$	−3.92385	−0.364321
$117$	1.00000	0.0924500
$118$	−3.38485	−0.311601
$119$	2.65040	0.242962
$120$	0	0
$121$	−0.471163	−0.0428330
$122$	3.14003	0.284285
$123$	−3.81681	−0.344150
$124$	−10.6873	−0.959752
$125$	0	0
$126$	0.816810	0.0727672
$127$	−0.183190	−0.0162555	−0.00812773	−	0.999967i	$-0.502587\pi$
$127$	−0.183190	−0.0162555	−0.00812773	+	0.999967i	$0.502587\pi$
$128$	−11.5328	−1.01936
$129$	10.0185	0.882077
$130$	0	0
$131$	−17.4504	−1.52465	−0.762326	−	0.647194i	$-0.775942\pi$
$131$	−17.4504	−1.52465	−0.762326	+	0.647194i	$0.775942\pi$
$132$	−5.42801	−0.472447
$133$	−2.59442	−0.224965
$134$	−5.89296	−0.509074
$135$	0	0
$136$	−3.89917	−0.334351
$137$	1.79834	0.153642	0.0768212	−	0.997045i	$-0.475523\pi$
$137$	1.79834	0.153642	0.0768212	+	0.997045i	$0.475523\pi$
$138$	−0.874485	−0.0744411
$139$	20.3249	1.72394	0.861968	−	0.506962i	$-0.169232\pi$
$139$	20.3249	1.72394	0.861968	+	0.506962i	$0.169232\pi$
$140$	0	0
$141$	11.2633	0.948540
$142$	−5.61515	−0.471213
$143$	3.24482	0.271345
$144$	2.14399	0.178666
$145$	0	0
$146$	3.04711	0.252181
$147$	−4.96080	−0.409160
$148$	−5.90312	−0.485234
$149$	−17.1809	−1.40752	−0.703758	−	0.710440i	$-0.748496\pi$
$149$	−17.1809	−1.40752	−0.703758	+	0.710440i	$0.748496\pi$
$150$	0	0
$151$	3.99605	0.325194	0.162597	−	0.986693i	$-0.448013\pi$
$151$	3.99605	0.325194	0.162597	+	0.986693i	$0.448013\pi$
$152$	3.81681	0.309584
$153$	1.85601	0.150050
$154$	2.65040	0.213575
$155$	0	0
$156$	−1.67282	−0.133933
$157$	7.67282	0.612358	0.306179	−	0.951974i	$-0.400949\pi$
$157$	7.67282	0.612358	0.306179	+	0.951974i	$0.400949\pi$
$158$	−1.69356	−0.134732
$159$	6.81681	0.540608
$160$	0	0
$161$	−2.18319	−0.172059
$162$	0.571993	0.0449400
$163$	0.471163	0.0369043	0.0184522	−	0.999830i	$-0.494126\pi$
$163$	0.471163	0.0369043	0.0184522	+	0.999830i	$0.494126\pi$
$164$	6.38485	0.498573
$165$	0	0
$166$	1.79608	0.139403
$167$	−18.7098	−1.44781	−0.723903	−	0.689902i	$-0.757654\pi$
$167$	−18.7098	−1.44781	−0.723903	+	0.689902i	$0.757654\pi$
$168$	−3.00000	−0.231455
$169$	1.00000	0.0769231
$170$	0	0
$171$	−1.81681	−0.138935
$172$	−16.7591	−1.27787
$173$	7.96080	0.605248	0.302624	−	0.953110i	$-0.402137\pi$
$173$	7.96080	0.605248	0.302624	+	0.953110i	$0.402137\pi$
$174$	1.34169	0.101714
$175$	0	0
$176$	6.95684	0.524392
$177$	−5.91764	−0.444797
$178$	−2.77761	−0.208190
$179$	15.6521	1.16989	0.584946	−	0.811072i	$-0.301116\pi$
$179$	15.6521	1.16989	0.584946	+	0.811072i	$0.301116\pi$
$180$	0	0
$181$	−24.5658	−1.82596	−0.912980	−	0.408004i	$-0.866225\pi$
$181$	−24.5658	−1.82596	−0.912980	+	0.408004i	$0.866225\pi$
$182$	0.816810	0.0605460
$183$	5.48963	0.405805
$184$	3.21183	0.236779
$185$	0	0
$186$	3.65435	0.267950
$187$	6.02242	0.440403
$188$	−18.8415	−1.37416
$189$	1.42801	0.103872
$190$	0	0
$191$	−21.0577	−1.52368	−0.761840	−	0.647765i	$-0.775704\pi$
$191$	−21.0577	−1.52368	−0.761840	+	0.647765i	$0.775704\pi$
$192$	−1.18319	−0.0853894
$193$	19.9401	1.43532	0.717659	−	0.696395i	$-0.245214\pi$
$193$	19.9401	1.43532	0.717659	+	0.696395i	$0.245214\pi$
$194$	0.863919	0.0620258
$195$	0	0
$196$	8.29854	0.592753
$197$	−23.4504	−1.67077	−0.835387	−	0.549662i	$-0.814756\pi$
$197$	−23.4504	−1.67077	−0.835387	+	0.549662i	$0.814756\pi$
$198$	1.85601	0.131901
$199$	16.2880	1.15462	0.577312	−	0.816524i	$-0.304102\pi$
$199$	16.2880	1.15462	0.577312	+	0.816524i	$0.304102\pi$
$200$	0	0
$201$	−10.3025	−0.726682
$202$	−9.73445	−0.684914
$203$	3.34960	0.235096
$204$	−3.10478	−0.217378
$205$	0	0
$206$	−5.56578	−0.387786
$207$	−1.52884	−0.106262
$208$	2.14399	0.148659
$209$	−5.89522	−0.407781
$210$	0	0
$211$	27.8538	1.91753	0.958766	−	0.284198i	$-0.0917272\pi$
$211$	27.8538	1.91753	0.958766	+	0.284198i	$0.0917272\pi$
$212$	−11.4033	−0.783183
$213$	−9.81681	−0.672637
$214$	−1.96306	−0.134192
$215$	0	0
$216$	−2.10083	−0.142943
$217$	9.12325	0.619327
$218$	−1.69356	−0.114702
$219$	5.32718	0.359977
$220$	0	0
$221$	1.85601	0.124849
$222$	2.01847	0.135471
$223$	11.1625	0.747493	0.373747	−	0.927531i	$-0.378073\pi$
$223$	11.1625	0.747493	0.373747	+	0.927531i	$0.378073\pi$
$224$	7.75123	0.517901
$225$	0	0
$226$	−5.46100	−0.363260
$227$	7.93611	0.526738	0.263369	−	0.964695i	$-0.415166\pi$
$227$	7.93611	0.526738	0.263369	+	0.964695i	$0.415166\pi$
$228$	3.03920	0.201276
$229$	27.9585	1.84755	0.923776	−	0.382933i	$-0.125086\pi$
$229$	27.9585	1.84755	0.923776	+	0.382933i	$0.125086\pi$
$230$	0	0
$231$	4.63362	0.304870
$232$	−4.92781	−0.323526
$233$	−1.14399	−0.0749450	−0.0374725	−	0.999298i	$-0.511931\pi$
$233$	−1.14399	−0.0749450	−0.0374725	+	0.999298i	$0.511931\pi$
$234$	0.571993	0.0373924
$235$	0	0
$236$	9.89917	0.644381
$237$	−2.96080	−0.192324
$238$	1.51601	0.0982684
$239$	−3.34960	−0.216668	−0.108334	−	0.994115i	$-0.534552\pi$
$239$	−3.34960	−0.216668	−0.108334	+	0.994115i	$0.534552\pi$
$240$	0	0
$241$	−8.09688	−0.521566	−0.260783	−	0.965397i	$-0.583981\pi$
$241$	−8.09688	−0.521566	−0.260783	+	0.965397i	$0.583981\pi$
$242$	−0.269502	−0.0173242
$243$	1.00000	0.0641500
$244$	−9.18319	−0.587893
$245$	0	0
$246$	−2.18319	−0.139195
$247$	−1.81681	−0.115601
$248$	−13.4218	−0.852285
$249$	3.14003	0.198992
$250$	0	0
$251$	−25.3641	−1.60097	−0.800484	−	0.599353i	$-0.795424\pi$
$251$	−25.3641	−1.60097	−0.800484	+	0.599353i	$0.795424\pi$
$252$	−2.38880	−0.150480
$253$	−4.96080	−0.311883
$254$	−0.104783	−0.00657469
$255$	0	0
$256$	−4.23030	−0.264394
$257$	19.5865	1.22177	0.610887	−	0.791718i	$-0.290813\pi$
$257$	19.5865	1.22177	0.610887	+	0.791718i	$0.290813\pi$
$258$	5.73050	0.356765
$259$	5.03920	0.313121
$260$	0	0
$261$	2.34565	0.145192
$262$	−9.98153	−0.616661
$263$	−7.24877	−0.446978	−0.223489	−	0.974706i	$-0.571745\pi$
$263$	−7.24877	−0.446978	−0.223489	+	0.974706i	$0.571745\pi$
$264$	−6.81681	−0.419546
$265$	0	0
$266$	−1.48399	−0.0909892
$267$	−4.85601	−0.297183
$268$	17.2343	1.05275
$269$	−14.5104	−0.884713	−0.442356	−	0.896839i	$-0.645857\pi$
$269$	−14.5104	−0.884713	−0.442356	+	0.896839i	$0.645857\pi$
$270$	0	0
$271$	−4.19771	−0.254993	−0.127496	−	0.991839i	$-0.540694\pi$
$271$	−4.19771	−0.254993	−0.127496	+	0.991839i	$0.540694\pi$
$272$	3.97927	0.241279
$273$	1.42801	0.0864269
$274$	1.02864	0.0621423
$275$	0	0
$276$	2.55748	0.153942
$277$	−16.6050	−0.997697	−0.498848	−	0.866689i	$-0.666244\pi$
$277$	−16.6050	−0.997697	−0.498848	+	0.866689i	$0.666244\pi$
$278$	11.6257	0.697264
$279$	6.38880	0.382488
$280$	0	0
$281$	24.3249	1.45110	0.725551	−	0.688168i	$-0.241585\pi$
$281$	24.3249	1.45110	0.725551	+	0.688168i	$0.241585\pi$
$282$	6.44252	0.383647
$283$	−7.71203	−0.458432	−0.229216	−	0.973376i	$-0.573616\pi$
$283$	−7.71203	−0.458432	−0.229216	+	0.973376i	$0.573616\pi$
$284$	16.4218	0.974454
$285$	0	0
$286$	1.85601	0.109748
$287$	−5.45043	−0.321729
$288$	5.42801	0.319848
$289$	−13.5552	−0.797366
$290$	0	0
$291$	1.51037	0.0885392
$292$	−8.91143	−0.521502
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−2.83754	−0.165489
$295$	0	0
$296$	−7.41349	−0.430900
$297$	3.24482	0.188283
$298$	−9.82738	−0.569285
$299$	−1.52884	−0.0884149
$300$	0	0
$301$	14.3064	0.824610
$302$	2.28571	0.131528
$303$	−17.0185	−0.977686
$304$	−3.89522	−0.223406
$305$	0	0
$306$	1.06163	0.0606892
$307$	−12.7882	−0.729860	−0.364930	−	0.931035i	$-0.618907\pi$
$307$	−12.7882	−0.729860	−0.364930	+	0.931035i	$0.618907\pi$
$308$	−7.75123	−0.441667
$309$	−9.73050	−0.553549
$310$	0	0
$311$	−18.0000	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	−2.10083	−0.118936
$313$	13.8824	0.784679	0.392340	−	0.919820i	$-0.371666\pi$
$313$	13.8824	0.784679	0.392340	+	0.919820i	$0.371666\pi$
$314$	4.38880	0.247675
$315$	0	0
$316$	4.95289	0.278622
$317$	8.01847	0.450362	0.225181	−	0.974317i	$-0.427703\pi$
$317$	8.01847	0.450362	0.225181	+	0.974317i	$0.427703\pi$
$318$	3.89917	0.218655
$319$	7.61120	0.426145
$320$	0	0
$321$	−3.43196	−0.191553
$322$	−1.24877	−0.0695912
$323$	−3.37202	−0.187624
$324$	−1.67282	−0.0929347
$325$	0	0
$326$	0.269502	0.0149263
$327$	−2.96080	−0.163732
$328$	8.01847	0.442746
$329$	16.0841	0.886742
$330$	0	0
$331$	−34.2201	−1.88091	−0.940454	−	0.339920i	$-0.889600\pi$
$331$	−34.2201	−1.88091	−0.940454	+	0.339920i	$0.889600\pi$
$332$	−5.25272	−0.288281
$333$	3.52884	0.193379
$334$	−10.7019	−0.585580
$335$	0	0
$336$	3.06163	0.167025
$337$	21.4712	1.16961	0.584804	−	0.811174i	$-0.301171\pi$
$337$	21.4712	1.16961	0.584804	+	0.811174i	$0.301171\pi$
$338$	0.571993	0.0311123
$339$	−9.54731	−0.518539
$340$	0	0
$341$	20.7305	1.12262
$342$	−1.03920	−0.0561937
$343$	−17.0801	−0.922239
$344$	−21.0471	−1.13478
$345$	0	0
$346$	4.55352	0.244799
$347$	−26.6129	−1.42865	−0.714327	−	0.699812i	$-0.753267\pi$
$347$	−26.6129	−1.42865	−0.714327	+	0.699812i	$0.753267\pi$
$348$	−3.92385	−0.210341
$349$	−13.8168	−0.739597	−0.369798	−	0.929112i	$-0.620573\pi$
$349$	−13.8168	−0.739597	−0.369798	+	0.929112i	$0.620573\pi$
$350$	0	0
$351$	1.00000	0.0533761
$352$	17.6129	0.938770
$353$	25.5288	1.35876	0.679381	−	0.733785i	$-0.262248\pi$
$353$	25.5288	1.35876	0.679381	+	0.733785i	$0.262248\pi$
$354$	−3.38485	−0.179903
$355$	0	0
$356$	8.12325	0.430532
$357$	2.65040	0.140274
$358$	8.95289	0.473175
$359$	4.65831	0.245856	0.122928	−	0.992416i	$-0.460772\pi$
$359$	4.65831	0.245856	0.122928	+	0.992416i	$0.460772\pi$
$360$	0	0
$361$	−15.6992	−0.826274
$362$	−14.0515	−0.738528
$363$	−0.471163	−0.0247296
$364$	−2.38880	−0.125207
$365$	0	0
$366$	3.14003	0.164132
$367$	−19.2672	−1.00574	−0.502871	−	0.864362i	$-0.667723\pi$
$367$	−19.2672	−1.00574	−0.502871	+	0.864362i	$0.667723\pi$
$368$	−3.27781	−0.170867
$369$	−3.81681	−0.198695
$370$	0	0
$371$	9.73445	0.505388
$372$	−10.6873	−0.554113
$373$	−6.12552	−0.317167	−0.158584	−	0.987346i	$-0.550693\pi$
$373$	−6.12552	−0.317167	−0.158584	+	0.987346i	$0.550693\pi$
$374$	3.44479	0.178126
$375$	0	0
$376$	−23.6623	−1.22029
$377$	2.34565	0.120807
$378$	0.816810	0.0420122
$379$	22.3104	1.14601	0.573004	−	0.819553i	$-0.305778\pi$
$379$	22.3104	1.14601	0.573004	+	0.819553i	$0.305778\pi$
$380$	0	0
$381$	−0.183190	−0.00938510
$382$	−12.0448	−0.616268
$383$	−37.0841	−1.89491	−0.947453	−	0.319894i	$-0.896353\pi$
$383$	−37.0841	−1.89491	−0.947453	+	0.319894i	$0.896353\pi$
$384$	−11.5328	−0.588530
$385$	0	0
$386$	11.4056	0.580529
$387$	10.0185	0.509268
$388$	−2.52658	−0.128267
$389$	−23.8353	−1.20850	−0.604248	−	0.796796i	$-0.706527\pi$
$389$	−23.8353	−1.20850	−0.604248	+	0.796796i	$0.706527\pi$
$390$	0	0
$391$	−2.83754	−0.143501
$392$	10.4218	0.526380
$393$	−17.4504	−0.880258
$394$	−13.4135	−0.675762
$395$	0	0
$396$	−5.42801	−0.272768
$397$	26.6992	1.33999	0.669997	−	0.742364i	$-0.266295\pi$
$397$	26.6992	1.33999	0.669997	+	0.742364i	$0.266295\pi$
$398$	9.31661	0.467000
$399$	−2.59442	−0.129883
$400$	0	0
$401$	21.8168	1.08948	0.544740	−	0.838605i	$-0.316628\pi$
$401$	21.8168	1.08948	0.544740	+	0.838605i	$0.316628\pi$
$402$	−5.89296	−0.293914
$403$	6.38880	0.318249
$404$	28.4689	1.41638
$405$	0	0
$406$	1.91595	0.0950869
$407$	11.4504	0.567577
$408$	−3.89917	−0.193038
$409$	−1.16246	−0.0574798	−0.0287399	−	0.999587i	$-0.509149\pi$
$409$	−1.16246	−0.0574798	−0.0287399	+	0.999587i	$0.509149\pi$
$410$	0	0
$411$	1.79834	0.0887055
$412$	16.2774	0.801930
$413$	−8.45043	−0.415819
$414$	−0.874485	−0.0429786
$415$	0	0
$416$	5.42801	0.266130
$417$	20.3249	0.995315
$418$	−3.37202	−0.164931
$419$	−2.46326	−0.120338	−0.0601690	−	0.998188i	$-0.519164\pi$
$419$	−2.46326	−0.120338	−0.0601690	+	0.998188i	$0.519164\pi$
$420$	0	0
$421$	27.6336	1.34678	0.673390	−	0.739287i	$-0.264837\pi$
$421$	27.6336	1.34678	0.673390	+	0.739287i	$0.264837\pi$
$422$	15.9322	0.775565
$423$	11.2633	0.547640
$424$	−14.3210	−0.695487
$425$	0	0
$426$	−5.61515	−0.272055
$427$	7.83923	0.379367
$428$	5.74106	0.277505
$429$	3.24482	0.156661
$430$	0	0
$431$	28.9114	1.39261	0.696307	−	0.717744i	$-0.254825\pi$
$431$	28.9114	1.39261	0.696307	+	0.717744i	$0.254825\pi$
$432$	2.14399	0.103153
$433$	−13.7569	−0.661113	−0.330557	−	0.943786i	$-0.607236\pi$
$433$	−13.7569	−0.661113	−0.330557	+	0.943786i	$0.607236\pi$
$434$	5.21844	0.250493
$435$	0	0
$436$	4.95289	0.237200
$437$	2.77761	0.132871
$438$	3.04711	0.145596
$439$	−30.5081	−1.45607	−0.728036	−	0.685539i	$-0.759567\pi$
$439$	−30.5081	−1.45607	−0.728036	+	0.685539i	$0.759567\pi$
$440$	0	0
$441$	−4.96080	−0.236228
$442$	1.06163	0.0504965
$443$	28.3064	1.34488	0.672440	−	0.740152i	$-0.265246\pi$
$443$	28.3064	1.34488	0.672440	+	0.740152i	$0.265246\pi$
$444$	−5.90312	−0.280150
$445$	0	0
$446$	6.38485	0.302331
$447$	−17.1809	−0.812630
$448$	−1.68960	−0.0798262
$449$	0.769701	0.0363244	0.0181622	−	0.999835i	$-0.494218\pi$
$449$	0.769701	0.0363244	0.0181622	+	0.999835i	$0.494218\pi$
$450$	0	0
$451$	−12.3849	−0.583180
$452$	15.9710	0.751211
$453$	3.99605	0.187751
$454$	4.53940	0.213045
$455$	0	0
$456$	3.81681	0.178739
$457$	15.0841	0.705602	0.352801	−	0.935698i	$-0.385229\pi$
$457$	15.0841	0.705602	0.352801	+	0.935698i	$0.385229\pi$
$458$	15.9921	0.747261
$459$	1.85601	0.0866313
$460$	0	0
$461$	10.3664	0.482810	0.241405	−	0.970424i	$-0.422392\pi$
$461$	10.3664	0.482810	0.241405	+	0.970424i	$0.422392\pi$
$462$	2.65040	0.123308
$463$	−8.06389	−0.374761	−0.187380	−	0.982287i	$-0.560000\pi$
$463$	−8.06389	−0.374761	−0.187380	+	0.982287i	$0.560000\pi$
$464$	5.02904	0.233467
$465$	0	0
$466$	−0.654353	−0.0303123
$467$	30.8145	1.42593	0.712964	−	0.701201i	$-0.247352\pi$
$467$	30.8145	1.42593	0.712964	+	0.701201i	$0.247352\pi$
$468$	−1.67282	−0.0773263
$469$	−14.7120	−0.679338
$470$	0	0
$471$	7.67282	0.353545
$472$	12.4320	0.572227
$473$	32.5081	1.49472
$474$	−1.69356	−0.0777876
$475$	0	0
$476$	−4.43365	−0.203216
$477$	6.81681	0.312120
$478$	−1.91595	−0.0876335
$479$	10.9938	0.502319	0.251159	−	0.967946i	$-0.419188\pi$
$479$	10.9938	0.502319	0.251159	+	0.967946i	$0.419188\pi$
$480$	0	0
$481$	3.52884	0.160901
$482$	−4.63136	−0.210953
$483$	−2.18319	−0.0993386
$484$	0.788172	0.0358260
$485$	0	0
$486$	0.571993	0.0259461
$487$	29.3602	1.33044	0.665218	−	0.746649i	$-0.268339\pi$
$487$	29.3602	1.33044	0.665218	+	0.746649i	$0.268339\pi$
$488$	−11.5328	−0.522065
$489$	0.471163	0.0213067
$490$	0	0
$491$	−21.0577	−0.950320	−0.475160	−	0.879900i	$-0.657610\pi$
$491$	−21.0577	−0.950320	−0.475160	+	0.879900i	$0.657610\pi$
$492$	6.38485	0.287851
$493$	4.35355	0.196074
$494$	−1.03920	−0.0467560
$495$	0	0
$496$	13.6975	0.615036
$497$	−14.0185	−0.628814
$498$	1.79608	0.0804842
$499$	23.8392	1.06719	0.533595	−	0.845740i	$-0.320841\pi$
$499$	23.8392	1.06719	0.533595	+	0.845740i	$0.320841\pi$
$500$	0	0
$501$	−18.7098	−0.835891
$502$	−14.5081	−0.647528
$503$	−21.8168	−0.972763	−0.486382	−	0.873746i	$-0.661684\pi$
$503$	−21.8168	−0.972763	−0.486382	+	0.873746i	$0.661684\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	−2.83754	−0.126144
$507$	1.00000	0.0444116
$508$	0.306444	0.0135963
$509$	2.01847	0.0894672	0.0447336	−	0.998999i	$-0.485756\pi$
$509$	2.01847	0.0894672	0.0447336	+	0.998999i	$0.485756\pi$
$510$	0	0
$511$	7.60724	0.336525
$512$	20.6459	0.912428
$513$	−1.81681	−0.0802141
$514$	11.2034	0.494159
$515$	0	0
$516$	−16.7591	−0.737780
$517$	36.5473	1.60735
$518$	2.88239	0.126645
$519$	7.96080	0.349440
$520$	0	0
$521$	5.02073	0.219962	0.109981	−	0.993934i	$-0.464921\pi$
$521$	5.02073	0.219962	0.109981	+	0.993934i	$0.464921\pi$
$522$	1.34169	0.0587244
$523$	18.5266	0.810111	0.405055	−	0.914292i	$-0.367252\pi$
$523$	18.5266	0.810111	0.405055	+	0.914292i	$0.367252\pi$
$524$	29.1915	1.27524
$525$	0	0
$526$	−4.14625	−0.180785
$527$	11.8577	0.516530
$528$	6.95684	0.302758
$529$	−20.6627	−0.898376
$530$	0	0
$531$	−5.91764	−0.256804
$532$	4.34000	0.188163
$533$	−3.81681	−0.165324
$534$	−2.77761	−0.120199
$535$	0	0
$536$	21.6438	0.934869
$537$	15.6521	0.675438
$538$	−8.29983	−0.357831
$539$	−16.0969	−0.693342
$540$	0	0
$541$	7.61515	0.327401	0.163700	−	0.986510i	$-0.447657\pi$
$541$	7.61515	0.327401	0.163700	+	0.986510i	$0.447657\pi$
$542$	−2.40106	−0.103134
$543$	−24.5658	−1.05422
$544$	10.0745	0.431939
$545$	0	0
$546$	0.816810	0.0349563
$547$	−17.9031	−0.765482	−0.382741	−	0.923856i	$-0.625020\pi$
$547$	−17.9031	−0.765482	−0.382741	+	0.923856i	$0.625020\pi$
$548$	−3.00830	−0.128508
$549$	5.48963	0.234292
$550$	0	0
$551$	−4.26160	−0.181550
$552$	3.21183	0.136704
$553$	−4.22804	−0.179794
$554$	−9.49794	−0.403529
$555$	0	0
$556$	−34.0000	−1.44192
$557$	−34.4218	−1.45850	−0.729249	−	0.684248i	$-0.760130\pi$
$557$	−34.4218	−1.45850	−0.729249	+	0.684248i	$0.760130\pi$
$558$	3.65435	0.154701
$559$	10.0185	0.423736
$560$	0	0
$561$	6.02242	0.254267
$562$	13.9137	0.586913
$563$	41.5658	1.75179	0.875894	−	0.482503i	$-0.160272\pi$
$563$	41.5658	1.75179	0.875894	+	0.482503i	$0.160272\pi$
$564$	−18.8415	−0.793370
$565$	0	0
$566$	−4.41123	−0.185418
$567$	1.42801	0.0599706
$568$	20.6235	0.865341
$569$	−26.0761	−1.09317	−0.546584	−	0.837404i	$-0.684072\pi$
$569$	−26.0761	−1.09317	−0.546584	+	0.837404i	$0.684072\pi$
$570$	0	0
$571$	3.41349	0.142850	0.0714250	−	0.997446i	$-0.477245\pi$
$571$	3.41349	0.142850	0.0714250	+	0.997446i	$0.477245\pi$
$572$	−5.42801	−0.226956
$573$	−21.0577	−0.879697
$574$	−3.11761	−0.130127
$575$	0	0
$576$	−1.18319	−0.0492996
$577$	5.10704	0.212609	0.106305	−	0.994334i	$-0.466098\pi$
$577$	5.10704	0.212609	0.106305	+	0.994334i	$0.466098\pi$
$578$	−7.75349	−0.322503
$579$	19.9401	0.828681
$580$	0	0
$581$	4.48399	0.186027
$582$	0.863919	0.0358106
$583$	22.1193	0.916088
$584$	−11.1915	−0.463107
$585$	0	0
$586$	3.43196	0.141773
$587$	−20.8705	−0.861419	−0.430710	−	0.902491i	$-0.641737\pi$
$587$	−20.8705	−0.861419	−0.430710	+	0.902491i	$0.641737\pi$
$588$	8.29854	0.342226
$589$	−11.6072	−0.478268
$590$	0	0
$591$	−23.4504	−0.964622
$592$	7.56578	0.310952
$593$	30.4403	1.25003	0.625016	−	0.780612i	$-0.285092\pi$
$593$	30.4403	1.25003	0.625016	+	0.780612i	$0.285092\pi$
$594$	1.85601	0.0761532
$595$	0	0
$596$	28.7407	1.17726
$597$	16.2880	0.666622
$598$	−0.874485	−0.0357603
$599$	11.5658	0.472565	0.236282	−	0.971684i	$-0.424071\pi$
$599$	11.5658	0.472565	0.236282	+	0.971684i	$0.424071\pi$
$600$	0	0
$601$	13.6728	0.557726	0.278863	−	0.960331i	$-0.410042\pi$
$601$	13.6728	0.557726	0.278863	+	0.960331i	$0.410042\pi$
$602$	8.18319	0.333522
$603$	−10.3025	−0.419550
$604$	−6.68468	−0.271996
$605$	0	0
$606$	−9.73445	−0.395435
$607$	15.4689	0.627863	0.313932	−	0.949446i	$-0.398354\pi$
$607$	15.4689	0.627863	0.313932	+	0.949446i	$0.398354\pi$
$608$	−9.86166	−0.399943
$609$	3.34960	0.135733
$610$	0	0
$611$	11.2633	0.455664
$612$	−3.10478	−0.125503
$613$	−0.287973	−0.0116311	−0.00581556	−	0.999983i	$-0.501851\pi$
$613$	−0.287973	−0.0116311	−0.00581556	+	0.999983i	$0.501851\pi$
$614$	−7.31475	−0.295199
$615$	0	0
$616$	−9.73445	−0.392212
$617$	6.28007	0.252826	0.126413	−	0.991978i	$-0.459654\pi$
$617$	6.28007	0.252826	0.126413	+	0.991978i	$0.459654\pi$
$618$	−5.56578	−0.223888
$619$	−20.6314	−0.829244	−0.414622	−	0.909994i	$-0.636086\pi$
$619$	−20.6314	−0.829244	−0.414622	+	0.909994i	$0.636086\pi$
$620$	0	0
$621$	−1.52884	−0.0613501
$622$	−10.2959	−0.412827
$623$	−6.93442	−0.277822
$624$	2.14399	0.0858282
$625$	0	0
$626$	7.94063	0.317372
$627$	−5.89522	−0.235432
$628$	−12.8353	−0.512183
$629$	6.54957	0.261148
$630$	0	0
$631$	−11.0392	−0.439464	−0.219732	−	0.975560i	$-0.570518\pi$
$631$	−11.0392	−0.439464	−0.219732	+	0.975560i	$0.570518\pi$
$632$	6.22013	0.247424
$633$	27.8538	1.10709
$634$	4.58651	0.182154
$635$	0	0
$636$	−11.4033	−0.452171
$637$	−4.96080	−0.196554
$638$	4.35355	0.172359
$639$	−9.81681	−0.388347
$640$	0	0
$641$	7.97136	0.314850	0.157425	−	0.987531i	$-0.449681\pi$
$641$	7.97136	0.314850	0.157425	+	0.987531i	$0.449681\pi$
$642$	−1.96306	−0.0774757
$643$	−39.5658	−1.56032	−0.780161	−	0.625579i	$-0.784863\pi$
$643$	−39.5658	−1.56032	−0.780161	+	0.625579i	$0.784863\pi$
$644$	3.65209	0.143913
$645$	0	0
$646$	−1.92878	−0.0758866
$647$	−24.6992	−0.971026	−0.485513	−	0.874230i	$-0.661367\pi$
$647$	−24.6992	−0.971026	−0.485513	+	0.874230i	$0.661367\pi$
$648$	−2.10083	−0.0825284
$649$	−19.2017	−0.753731
$650$	0	0
$651$	9.12325	0.357569
$652$	−0.788172	−0.0308672
$653$	37.7361	1.47673	0.738365	−	0.674402i	$-0.235598\pi$
$653$	37.7361	1.47673	0.738365	+	0.674402i	$0.235598\pi$
$654$	−1.69356	−0.0662233
$655$	0	0
$656$	−8.18319	−0.319500
$657$	5.32718	0.207833
$658$	9.19997	0.358652
$659$	−49.6890	−1.93561	−0.967805	−	0.251701i	$-0.919010\pi$
$659$	−49.6890	−1.93561	−0.967805	+	0.251701i	$0.919010\pi$
$660$	0	0
$661$	40.6235	1.58007	0.790035	−	0.613062i	$-0.210063\pi$
$661$	40.6235	1.58007	0.790035	+	0.613062i	$0.210063\pi$
$662$	−19.5737	−0.760753
$663$	1.85601	0.0720816
$664$	−6.59668	−0.256001
$665$	0	0
$666$	2.01847	0.0782142
$667$	−3.58611	−0.138855
$668$	31.2981	1.21096
$669$	11.1625	0.431566
$670$	0	0
$671$	17.8129	0.687658
$672$	7.75123	0.299010
$673$	−17.7961	−0.685988	−0.342994	−	0.939338i	$-0.611441\pi$
$673$	−17.7961	−0.685988	−0.342994	+	0.939338i	$0.611441\pi$
$674$	12.2814	0.473060
$675$	0	0
$676$	−1.67282	−0.0643394
$677$	−24.8850	−0.956410	−0.478205	−	0.878248i	$-0.658712\pi$
$677$	−24.8850	−0.956410	−0.478205	+	0.878248i	$0.658712\pi$
$678$	−5.46100	−0.209728
$679$	2.15681	0.0827709
$680$	0	0
$681$	7.93611	0.304112
$682$	11.8577	0.454055
$683$	−27.3602	−1.04691	−0.523454	−	0.852054i	$-0.675357\pi$
$683$	−27.3602	−1.04691	−0.523454	+	0.852054i	$0.675357\pi$
$684$	3.03920	0.116207
$685$	0	0
$686$	−9.76970	−0.373009
$687$	27.9585	1.06668
$688$	21.4795	0.818897
$689$	6.81681	0.259700
$690$	0	0
$691$	20.2919	0.771941	0.385971	−	0.922511i	$-0.373867\pi$
$691$	20.2919	0.771941	0.385971	+	0.922511i	$0.373867\pi$
$692$	−13.3170	−0.506237
$693$	4.63362	0.176017
$694$	−15.2224	−0.577834
$695$	0	0
$696$	−4.92781	−0.186788
$697$	−7.08405	−0.268328
$698$	−7.90312	−0.299138
$699$	−1.14399	−0.0432695
$700$	0	0
$701$	40.1888	1.51791	0.758956	−	0.651142i	$-0.225710\pi$
$701$	40.1888	1.51791	0.758956	+	0.651142i	$0.225710\pi$
$702$	0.571993	0.0215885
$703$	−6.41123	−0.241804
$704$	−3.83923	−0.144697
$705$	0	0
$706$	14.6023	0.549566
$707$	−24.3025	−0.913989
$708$	9.89917	0.372034
$709$	20.9898	0.788290	0.394145	−	0.919048i	$-0.371041\pi$
$709$	20.9898	0.788290	0.394145	+	0.919048i	$0.371041\pi$
$710$	0	0
$711$	−2.96080	−0.111039
$712$	10.2017	0.382323
$713$	−9.76744	−0.365794
$714$	1.51601	0.0567353
$715$	0	0
$716$	−26.1832	−0.978512
$717$	−3.34960	−0.125093
$718$	2.66452	0.0994390
$719$	6.47907	0.241628	0.120814	−	0.992675i	$-0.461449\pi$
$719$	6.47907	0.241628	0.120814	+	0.992675i	$0.461449\pi$
$720$	0	0
$721$	−13.8952	−0.517485
$722$	−8.97984	−0.334195
$723$	−8.09688	−0.301126
$724$	41.0942	1.52725
$725$	0	0
$726$	−0.269502	−0.0100022
$727$	−22.7098	−0.842259	−0.421129	−	0.907001i	$-0.638366\pi$
$727$	−22.7098	−0.842259	−0.421129	+	0.907001i	$0.638366\pi$
$728$	−3.00000	−0.111187
$729$	1.00000	0.0370370
$730$	0	0
$731$	18.5944	0.687739
$732$	−9.18319	−0.339420
$733$	−43.0577	−1.59037	−0.795186	−	0.606366i	$-0.792627\pi$
$733$	−43.0577	−1.59037	−0.795186	+	0.606366i	$0.792627\pi$
$734$	−11.0207	−0.406783
$735$	0	0
$736$	−8.29854	−0.305888
$737$	−33.4297	−1.23140
$738$	−2.18319	−0.0803643
$739$	−38.4337	−1.41380	−0.706902	−	0.707311i	$-0.749908\pi$
$739$	−38.4337	−1.41380	−0.706902	+	0.707311i	$0.749908\pi$
$740$	0	0
$741$	−1.81681	−0.0667422
$742$	5.56804	0.204409
$743$	18.2320	0.668867	0.334433	−	0.942419i	$-0.391455\pi$
$743$	18.2320	0.668867	0.334433	+	0.942419i	$0.391455\pi$
$744$	−13.4218	−0.492067
$745$	0	0
$746$	−3.50375	−0.128282
$747$	3.14003	0.114888
$748$	−10.0745	−0.368359
$749$	−4.90086	−0.179074
$750$	0	0
$751$	−25.3720	−0.925838	−0.462919	−	0.886401i	$-0.653198\pi$
$751$	−25.3720	−0.925838	−0.462919	+	0.886401i	$0.653198\pi$
$752$	24.1483	0.880599
$753$	−25.3641	−0.924320
$754$	1.34169	0.0488616
$755$	0	0
$756$	−2.38880	−0.0868799
$757$	−32.1888	−1.16992	−0.584962	−	0.811061i	$-0.698890\pi$
$757$	−32.1888	−1.16992	−0.584962	+	0.811061i	$0.698890\pi$
$758$	12.7614	0.463515
$759$	−4.96080	−0.180066
$760$	0	0
$761$	32.2280	1.16827	0.584133	−	0.811658i	$-0.301435\pi$
$761$	32.2280	1.16827	0.584133	+	0.811658i	$0.301435\pi$
$762$	−0.104783	−0.00379590
$763$	−4.22804	−0.153065
$764$	35.2258	1.27442
$765$	0	0
$766$	−21.2118	−0.766414
$767$	−5.91764	−0.213674
$768$	−4.23030	−0.152648
$769$	39.5843	1.42744	0.713722	−	0.700429i	$-0.247008\pi$
$769$	39.5843	1.42744	0.713722	+	0.700429i	$0.247008\pi$
$770$	0	0
$771$	19.5865	0.705391
$772$	−33.3562	−1.20052
$773$	−19.4689	−0.700248	−0.350124	−	0.936703i	$-0.613861\pi$
$773$	−19.4689	−0.700248	−0.350124	+	0.936703i	$0.613861\pi$
$774$	5.73050	0.205978
$775$	0	0
$776$	−3.17302	−0.113905
$777$	5.03920	0.180780
$778$	−13.6336	−0.488789
$779$	6.93442	0.248451
$780$	0	0
$781$	−31.8538	−1.13982
$782$	−1.62306	−0.0580403
$783$	2.34565	0.0838266
$784$	−10.6359	−0.379853
$785$	0	0
$786$	−9.98153	−0.356029
$787$	−17.0722	−0.608558	−0.304279	−	0.952583i	$-0.598416\pi$
$787$	−17.0722	−0.608558	−0.304279	+	0.952583i	$0.598416\pi$
$788$	39.2284	1.39746
$789$	−7.24877	−0.258063
$790$	0	0
$791$	−13.6336	−0.484756
$792$	−6.81681	−0.242225
$793$	5.48963	0.194943
$794$	15.2718	0.541975
$795$	0	0
$796$	−27.2469	−0.965741
$797$	17.5187	0.620543	0.310272	−	0.950648i	$-0.399580\pi$
$797$	17.5187	0.620543	0.310272	+	0.950648i	$0.399580\pi$
$798$	−1.48399	−0.0525326
$799$	20.9048	0.739559
$800$	0	0
$801$	−4.85601	−0.171579
$802$	12.4791	0.440651
$803$	17.2857	0.610000
$804$	17.2343	0.607805
$805$	0	0
$806$	3.65435	0.128719
$807$	−14.5104	−0.510789
$808$	35.7529	1.25778
$809$	16.2017	0.569620	0.284810	−	0.958584i	$-0.408069\pi$
$809$	16.2017	0.569620	0.284810	+	0.958584i	$0.408069\pi$
$810$	0	0
$811$	21.5513	0.756767	0.378384	−	0.925649i	$-0.376480\pi$
$811$	21.5513	0.756767	0.378384	+	0.925649i	$0.376480\pi$
$812$	−5.60329	−0.196637
$813$	−4.19771	−0.147220
$814$	6.54957	0.229562
$815$	0	0
$816$	3.97927	0.139302
$817$	−18.2017	−0.636796
$818$	−0.664918	−0.0232483
$819$	1.42801	0.0498986
$820$	0	0
$821$	31.5288	1.10036	0.550182	−	0.835045i	$-0.314558\pi$
$821$	31.5288	1.10036	0.550182	+	0.835045i	$0.314558\pi$
$822$	1.02864	0.0358779
$823$	−56.1971	−1.95891	−0.979455	−	0.201665i	$-0.935365\pi$
$823$	−56.1971	−1.95891	−0.979455	+	0.201665i	$0.935365\pi$
$824$	20.4421	0.712135
$825$	0	0
$826$	−4.83359	−0.168182
$827$	−51.5697	−1.79326	−0.896628	−	0.442785i	$-0.853990\pi$
$827$	−51.5697	−1.79326	−0.896628	+	0.442785i	$0.853990\pi$
$828$	2.55748	0.0888784
$829$	−14.0286	−0.487235	−0.243617	−	0.969871i	$-0.578334\pi$
$829$	−14.0286	−0.487235	−0.243617	+	0.969871i	$0.578334\pi$
$830$	0	0
$831$	−16.6050	−0.576020
$832$	−1.18319	−0.0410197
$833$	−9.20731	−0.319014
$834$	11.6257	0.402566
$835$	0	0
$836$	9.86166	0.341073
$837$	6.38880	0.220829
$838$	−1.40897	−0.0486719
$839$	−28.4712	−0.982934	−0.491467	−	0.870896i	$-0.663539\pi$
$839$	−28.4712	−0.982934	−0.491467	+	0.870896i	$0.663539\pi$
$840$	0	0
$841$	−23.4979	−0.810274
$842$	15.8062	0.544719
$843$	24.3249	0.837795
$844$	−46.5944	−1.60385
$845$	0	0
$846$	6.44252	0.221499
$847$	−0.672824	−0.0231185
$848$	14.6151	0.501886
$849$	−7.71203	−0.264676
$850$	0	0
$851$	−5.39502	−0.184939
$852$	16.4218	0.562601
$853$	−33.5552	−1.14891	−0.574454	−	0.818537i	$-0.694786\pi$
$853$	−33.5552	−1.14891	−0.574454	+	0.818537i	$0.694786\pi$
$854$	4.48399	0.153439
$855$	0	0
$856$	7.20997	0.246432
$857$	37.8432	1.29270	0.646349	−	0.763042i	$-0.276295\pi$
$857$	37.8432	1.29270	0.646349	+	0.763042i	$0.276295\pi$
$858$	1.85601	0.0633633
$859$	14.3849	0.490805	0.245402	−	0.969421i	$-0.421080\pi$
$859$	14.3849	0.490805	0.245402	+	0.969421i	$0.421080\pi$
$860$	0	0
$861$	−5.45043	−0.185750
$862$	16.5371	0.563257
$863$	32.2610	1.09818	0.549089	−	0.835764i	$-0.314975\pi$
$863$	32.2610	1.09818	0.549089	+	0.835764i	$0.314975\pi$
$864$	5.42801	0.184665
$865$	0	0
$866$	−7.86884	−0.267394
$867$	−13.5552	−0.460359
$868$	−15.2616	−0.518012
$869$	−9.60724	−0.325903
$870$	0	0
$871$	−10.3025	−0.349087
$872$	6.22013	0.210640
$873$	1.51037	0.0511181
$874$	1.58877	0.0537410
$875$	0	0
$876$	−8.91143	−0.301089
$877$	57.6996	1.94838	0.974189	−	0.225736i	$-0.0724787\pi$
$877$	57.6996	1.94838	0.974189	+	0.225736i	$0.0724787\pi$
$878$	−17.4504	−0.588924
$879$	6.00000	0.202375
$880$	0	0
$881$	−56.6811	−1.90964	−0.954818	−	0.297192i	$-0.903950\pi$
$881$	−56.6811	−1.90964	−0.954818	+	0.297192i	$0.903950\pi$
$882$	−2.83754	−0.0955450
$883$	−20.0863	−0.675958	−0.337979	−	0.941154i	$-0.609743\pi$
$883$	−20.0863	−0.675958	−0.337979	+	0.941154i	$0.609743\pi$
$884$	−3.10478	−0.104425
$885$	0	0
$886$	16.1911	0.543950
$887$	−17.2857	−0.580397	−0.290199	−	0.956966i	$-0.593721\pi$
$887$	−17.2857	−0.580397	−0.290199	+	0.956966i	$0.593721\pi$
$888$	−7.41349	−0.248780
$889$	−0.261596	−0.00877366
$890$	0	0
$891$	3.24482	0.108705
$892$	−18.6728	−0.625212
$893$	−20.4633	−0.684777
$894$	−9.82738	−0.328677
$895$	0	0
$896$	−16.4689	−0.550187
$897$	−1.52884	−0.0510464
$898$	0.440264	0.0146918
$899$	14.9859	0.499807
$900$	0	0
$901$	12.6521	0.421502
$902$	−7.08405	−0.235873
$903$	14.3064	0.476089
$904$	20.0573	0.667095
$905$	0	0
$906$	2.28571	0.0759377
$907$	−48.4033	−1.60721	−0.803603	−	0.595166i	$-0.797086\pi$
$907$	−48.4033	−1.60721	−0.803603	+	0.595166i	$0.797086\pi$
$908$	−13.2757	−0.440570
$909$	−17.0185	−0.564467
$910$	0	0
$911$	−9.16246	−0.303566	−0.151783	−	0.988414i	$-0.548501\pi$
$911$	−9.16246	−0.303566	−0.151783	+	0.988414i	$0.548501\pi$
$912$	−3.89522	−0.128984
$913$	10.1888	0.337201
$914$	8.62798	0.285388
$915$	0	0
$916$	−46.7697	−1.54531
$917$	−24.9193	−0.822909
$918$	1.06163	0.0350389
$919$	7.06558	0.233072	0.116536	−	0.993186i	$-0.462821\pi$
$919$	7.06558	0.233072	0.116536	+	0.993186i	$0.462821\pi$
$920$	0	0
$921$	−12.7882	−0.421385
$922$	5.92950	0.195278
$923$	−9.81681	−0.323124
$924$	−7.75123	−0.254997
$925$	0	0
$926$	−4.61249	−0.151576
$927$	−9.73050	−0.319591
$928$	12.7322	0.417955
$929$	37.3042	1.22391	0.611955	−	0.790892i	$-0.290383\pi$
$929$	37.3042	1.22391	0.611955	+	0.790892i	$0.290383\pi$
$930$	0	0
$931$	9.01283	0.295383
$932$	1.91369	0.0626849
$933$	−18.0000	−0.589294
$934$	17.6257	0.576731
$935$	0	0
$936$	−2.10083	−0.0686678
$937$	−18.8353	−0.615322	−0.307661	−	0.951496i	$-0.599546\pi$
$937$	−18.8353	−0.615322	−0.307661	+	0.951496i	$0.599546\pi$
$938$	−8.41518	−0.274765
$939$	13.8824	0.453035
$940$	0	0
$941$	−53.6106	−1.74766	−0.873828	−	0.486235i	$-0.838370\pi$
$941$	−53.6106	−1.74766	−0.873828	+	0.486235i	$0.838370\pi$
$942$	4.38880	0.142995
$943$	5.83528	0.190023
$944$	−12.6873	−0.412938
$945$	0	0
$946$	18.5944	0.604557
$947$	−12.6319	−0.410483	−0.205241	−	0.978711i	$-0.565798\pi$
$947$	−12.6319	−0.410483	−0.205241	+	0.978711i	$0.565798\pi$
$948$	4.95289	0.160862
$949$	5.32718	0.172927
$950$	0	0
$951$	8.01847	0.260017
$952$	−5.56804	−0.180461
$953$	58.8044	1.90486	0.952430	−	0.304756i	$-0.0985750\pi$
$953$	58.8044	1.90486	0.952430	+	0.304756i	$0.0985750\pi$
$954$	3.89917	0.126240
$955$	0	0
$956$	5.60329	0.181223
$957$	7.61120	0.246035
$958$	6.28837	0.203168
$959$	2.56804	0.0829263
$960$	0	0
$961$	9.81681	0.316671
$962$	2.01847	0.0650781
$963$	−3.43196	−0.110593
$964$	13.5446	0.436244
$965$	0	0
$966$	−1.24877	−0.0401785
$967$	−6.43027	−0.206783	−0.103392	−	0.994641i	$-0.532970\pi$
$967$	−6.43027	−0.206783	−0.103392	+	0.994641i	$0.532970\pi$
$968$	0.989833	0.0318144
$969$	−3.37202	−0.108325
$970$	0	0
$971$	0.604983	0.0194148	0.00970741	−	0.999953i	$-0.496910\pi$
$971$	0.604983	0.0194148	0.00970741	+	0.999953i	$0.496910\pi$
$972$	−1.67282	−0.0536558
$973$	29.0241	0.930470
$974$	16.7938	0.538109
$975$	0	0
$976$	11.7697	0.376739
$977$	−4.36638	−0.139693	−0.0698464	−	0.997558i	$-0.522251\pi$
$977$	−4.36638	−0.139693	−0.0698464	+	0.997558i	$0.522251\pi$
$978$	0.269502	0.00861772
$979$	−15.7569	−0.503592
$980$	0	0
$981$	−2.96080	−0.0945310
$982$	−12.0448	−0.384367
$983$	−30.3025	−0.966499	−0.483250	−	0.875483i	$-0.660544\pi$
$983$	−30.3025	−0.966499	−0.483250	+	0.875483i	$0.660544\pi$
$984$	8.01847	0.255620
$985$	0	0
$986$	2.49020	0.0793042
$987$	16.0841	0.511961
$988$	3.03920	0.0966899
$989$	−15.3166	−0.487040
$990$	0	0
$991$	−4.96870	−0.157836	−0.0789180	−	0.996881i	$-0.525147\pi$
$991$	−4.96870	−0.157836	−0.0789180	+	0.996881i	$0.525147\pi$
$992$	34.6785	1.10104
$993$	−34.2201	−1.08594
$994$	−8.01847	−0.254330
$995$	0	0
$996$	−5.25272	−0.166439
$997$	−11.2959	−0.357744	−0.178872	−	0.983872i	$-0.557245\pi$
$997$	−11.2959	−0.357744	−0.178872	+	0.983872i	$0.557245\pi$
$998$	13.6359	0.431636
$999$	3.52884	0.111647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.a.p.1.2	yes	3
3.2	odd	2		2925.2.a.bg.1.2		3
5.2	odd	4		975.2.c.j.274.4		6
5.3	odd	4		975.2.c.j.274.3		6
5.4	even	2		975.2.a.n.1.2	✓	3
15.2	even	4		2925.2.c.x.2224.3		6
15.8	even	4		2925.2.c.x.2224.4		6
15.14	odd	2		2925.2.a.bi.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.a.n.1.2	✓	3	5.4	even	2
975.2.a.p.1.2	yes	3	1.1	even	1	trivial
975.2.c.j.274.3		6	5.3	odd	4
975.2.c.j.274.4		6	5.2	odd	4
2925.2.a.bg.1.2		3	3.2	odd	2
2925.2.a.bi.1.2		3	15.14	odd	2
2925.2.c.x.2224.3		6	15.2	even	4
2925.2.c.x.2224.4		6	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.a (trivial)

\(f(q)\)	\(=\)	\(q+0.571993 q^{2} +1.00000 q^{3} -1.67282 q^{4} +0.571993 q^{6} +1.42801 q^{7} -2.10083 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.571993 q^{2} +1.00000 q^{3} -1.67282 q^{4} +0.571993 q^{6} +1.42801 q^{7} -2.10083 q^{8} +1.00000 q^{9} +3.24482 q^{11} -1.67282 q^{12} +1.00000 q^{13} +0.816810 q^{14} +2.14399 q^{16} +1.85601 q^{17} +0.571993 q^{18} -1.81681 q^{19} +1.42801 q^{21} +1.85601 q^{22} -1.52884 q^{23} -2.10083 q^{24} +0.571993 q^{26} +1.00000 q^{27} -2.38880 q^{28} +2.34565 q^{29} +6.38880 q^{31} +5.42801 q^{32} +3.24482 q^{33} +1.06163 q^{34} -1.67282 q^{36} +3.52884 q^{37} -1.03920 q^{38} +1.00000 q^{39} -3.81681 q^{41} +0.816810 q^{42} +10.0185 q^{43} -5.42801 q^{44} -0.874485 q^{46} +11.2633 q^{47} +2.14399 q^{48} -4.96080 q^{49} +1.85601 q^{51} -1.67282 q^{52} +6.81681 q^{53} +0.571993 q^{54} -3.00000 q^{56} -1.81681 q^{57} +1.34169 q^{58} -5.91764 q^{59} +5.48963 q^{61} +3.65435 q^{62} +1.42801 q^{63} -1.18319 q^{64} +1.85601 q^{66} -10.3025 q^{67} -3.10478 q^{68} -1.52884 q^{69} -9.81681 q^{71} -2.10083 q^{72} +5.32718 q^{73} +2.01847 q^{74} +3.03920 q^{76} +4.63362 q^{77} +0.571993 q^{78} -2.96080 q^{79} +1.00000 q^{81} -2.18319 q^{82} +3.14003 q^{83} -2.38880 q^{84} +5.73050 q^{86} +2.34565 q^{87} -6.81681 q^{88} -4.85601 q^{89} +1.42801 q^{91} +2.55748 q^{92} +6.38880 q^{93} +6.44252 q^{94} +5.42801 q^{96} +1.51037 q^{97} -2.83754 q^{98} +3.24482 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + 5 q^{4} + q^{6} + 5 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + 5 * q^4 + q^6 + 5 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + 5 q^{4} + q^{6} + 5 q^{7} + 3 q^{8} + 3 q^{9} - q^{11} + 5 q^{12} + 3 q^{13} - 9 q^{14} + 5 q^{16} + 7 q^{17} + q^{18} + 6 q^{19} + 5 q^{21} + 7 q^{22} + 4 q^{23} + 3 q^{24} + q^{26} + 3 q^{27} + 5 q^{28} - 13 q^{29} + 7 q^{31} + 17 q^{32} - q^{33} - 19 q^{34} + 5 q^{36} + 2 q^{37} - 16 q^{38} + 3 q^{39} - 9 q^{42} - 17 q^{44} + 26 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} + 7 q^{51} + 5 q^{52} + 9 q^{53} + q^{54} - 9 q^{56} + 6 q^{57} - 11 q^{58} + 3 q^{59} - 5 q^{61} + 31 q^{62} + 5 q^{63} - 15 q^{64} + 7 q^{66} - 3 q^{67} + 5 q^{68} + 4 q^{69} - 18 q^{71} + 3 q^{72} + 26 q^{73} - 24 q^{74} + 22 q^{76} - 9 q^{77} + q^{78} + 4 q^{79} + 3 q^{81} - 18 q^{82} + 13 q^{83} + 5 q^{84} - 10 q^{86} - 13 q^{87} - 9 q^{88} - 16 q^{89} + 5 q^{91} + 32 q^{92} + 7 q^{93} - 5 q^{94} + 17 q^{96} + 26 q^{97} - 40 q^{98} - q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + 5 * q^4 + q^6 + 5 * q^7 + 3 * q^8 + 3 * q^9 - q^11 + 5 * q^12 + 3 * q^13 - 9 * q^14 + 5 * q^16 + 7 * q^17 + q^18 + 6 * q^19 + 5 * q^21 + 7 * q^22 + 4 * q^23 + 3 * q^24 + q^26 + 3 * q^27 + 5 * q^28 - 13 * q^29 + 7 * q^31 + 17 * q^32 - q^33 - 19 * q^34 + 5 * q^36 + 2 * q^37 - 16 * q^38 + 3 * q^39 - 9 * q^42 - 17 * q^44 + 26 * q^46 - 7 * q^47 + 5 * q^48 - 2 * q^49 + 7 * q^51 + 5 * q^52 + 9 * q^53 + q^54 - 9 * q^56 + 6 * q^57 - 11 * q^58 + 3 * q^59 - 5 * q^61 + 31 * q^62 + 5 * q^63 - 15 * q^64 + 7 * q^66 - 3 * q^67 + 5 * q^68 + 4 * q^69 - 18 * q^71 + 3 * q^72 + 26 * q^73 - 24 * q^74 + 22 * q^76 - 9 * q^77 + q^78 + 4 * q^79 + 3 * q^81 - 18 * q^82 + 13 * q^83 + 5 * q^84 - 10 * q^86 - 13 * q^87 - 9 * q^88 - 16 * q^89 + 5 * q^91 + 32 * q^92 + 7 * q^93 - 5 * q^94 + 17 * q^96 + 26 * q^97 - 40 * q^98 - q^99

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